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I was wondering about how to find current density, given a resistor and an electromotive force.

resistor's data are: resistivity = $\rho$, length = $l$, and cross sectional area = $A$. resistor = $\rho * \frac{l}{A}$. electromotive force is equal to Ohm's law, $EMF = R*I$, but I need to use microscopic version of Ohm's law, because I need to find current density. $E = \rho * j$, and therefore current density is equal to $j = \frac{E}{\rho}$, I have a question:

is $E$ equal to $EMF$? why? why not?

if they are the same thing, then I can use microscopic version of Ohm's law, I know $EMF = E$, and I know $EMF$. Otherwise I don't know what to do in order to find $E$.

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    $\begingroup$ Electromotive force comes from a battery or a voltage source. If you connect your resistor to the battery it will be responsible for a current flow an $V_{bat} = I \cdot R = E \cdot l $ $\endgroup$ Jul 10, 2022 at 9:47
  • $\begingroup$ $E = \frac{I*R}{l} = V_(bat)$, right? okay, it was just algebra $\endgroup$ Jul 10, 2022 at 9:56
  • $\begingroup$ not right V=IR not IR/L $\endgroup$
    – trula
    Jul 10, 2022 at 9:59
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    $\begingroup$ EMF and electric potential (Voltage, V) have the same effect on charges, so they are generally numerically equal. $\endgroup$
    – garyp
    Jul 10, 2022 at 11:21
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    $\begingroup$ in your definition $E l = V$ $\endgroup$ Jul 11, 2022 at 11:42

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For current density just use I/A or E=U/L

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  • $\begingroup$ what does U stand for? $\endgroup$ Jul 10, 2022 at 10:09
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    $\begingroup$ @GabrielBurzacchini U is European for potential difference. $\endgroup$
    – The Photon
    Jul 10, 2022 at 14:58

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